A note on some filters in residuated lattices

作者：Xiao, Lei; Liu, Lianzhen^*

来源：Journal of Intelligent and Fuzzy Systems, 2016, 30(1): 493-500.

DOI：10.3233/IFS-151774

• Residuated lattice
• EIMTL-filter
• associative filter
• t-filter

Recently, the notions of EIMTL-filters, associative filters, t-filters and I-filters were introduced in MTL-algebras and residuated lattices, respectively. In this paper, we consider these filters in residuated lattices and study some properties of them. We prove that t-filters and I-filters coincide in residuated lattices. The conditions under which an EIMTL-filter is a t-filter, and under which a residuated lattice has a proper associative filter are established. We also study the existence of a proper EIMTL-filter and prove that every maximal filter is an EIMTL-filter, and hence all residuated lattices have proper EIMTL-filters.

• 出版日期2016
• 单位江南大学